Three departments of a company employ a total of 1274 people. The second department employs 70 more people than the first one, and the third department employs 84 more workers than the second one. How many people work in each department?
Let's call the number of people in the first department "x".
The second department employs 70 more people than the first one, so this means the second department has "x + 70" people.
The third department employs 84 more workers than the second one, so this means the third department has "x + 70 + 84" people.
Given that the total number of people in all three departments is 1274, we can set up the following equation:
x + (x + 70) + (x + 70 + 84) = 1274
Simplifying the equation:
3x + 224 = 1274
Subtracting 224 from both sides of the equation:
3x = 1274 - 224
3x = 1050
Dividing both sides of the equation by 3:
x = 1050 / 3
x = 350
So, the first department has 350 people, the second department has 350 + 70 = 420 people, and the third department has 420 + 84 = 504 people.
To solve this problem, let's assign variables to the number of people in each department. Let's say the number of people in the first department is x.
According to the problem, the second department employs 70 more people than the first one. So, the number of people in the second department would be x + 70.
Similarly, the third department employs 84 more people than the second one. So, the number of people in the third department would be (x + 70) + 84.
Now, we can set up an equation to represent the total number of people in all three departments. The sum of the number of people in each department should be equal to the total number of people, which is 1274.
x + (x + 70) + ((x + 70) + 84) = 1274
Simplifying the equation, we have:
x + x + 70 + x + 70 + 84 = 1274
Combining like terms, we get:
3x + 224 = 1274
Next, let's isolate the variable by subtracting 224 from both sides of the equation:
3x = 1274 - 224
3x = 1050
Finally, we'll divide both sides of the equation by 3 to solve for x:
x = 1050 / 3
x = 350
So, the first department employs 350 people.
Substituting this value back into the expressions we made earlier, we find that the second department employs 350 + 70 = 420 people, and the third department employs (350 + 70) + 84 = 504 people.
Therefore, the number of people in each department is as follows:
First department: 350 people
Second department: 420 people
Third department: 504 people.
how did applea privusume spilled perfume +actions swit
D1 + D2 + D3 = 1274
D1 + 70 = D2
D2 + 84 = D3
solve the system